The section of the star which is facing the planet with life is left uncovered to let the planet receive enough light
This is slightly more awkward than you might think, on account of the elements of the swarm orbiting the sun at a different rate to the planet (because their orbital radii are so different).
On Earth you can create things like sun-synchronous orbits which [precess] 2 with a period of a year, but that relies on the Earth being a slightly squashed shape and the Sun is just too round to be able to pull tricks like that.
This means you'll either have to have quite a sparse swarm (eg. wide orbital radius, wide spacing between elements) or the elements will need a way to let light past when they'd otherwise shade the planet.
the rest of star is surrounded by a Dyson swarm in the shape of some sort of creature of their choosing.
This will definitely need the elements to have some kind of ability to change their habit of reflecting/occluding light. As the swarm elements transit the sun, they either need to rotate their collecting surfaces so they're parallel to the light rays directed at the planet, or they need to render them somehow transparent (like venetian blinds, perhaps) so they let enough sunlight past.
Whatever trick they use, the same approach can be used to modulate the silhouette of the swarm (by selectively letting some starlight past, or by deliberately rotating the collectors away from the sun to block starlight directed at the planet) or to deliberately reflect additional sunlight towards the planet.
How visible would this Dyson swarm "creature" be on the planet at any time of the day
Elements that appear to be close to the sun but not actually occluding it will be more or less invisible, most of the time. Special circumstances like solar eclipses by a suitable nearby body that doesn't also wholly occlude the swarm would work very well (and a monster head that appeared during a solar eclipse would certainly be one for the history books) but general observation will have to wait for the invention of the coronagraph, which is not an easy thing to discover.
After sunset, or before sunrise, a wide enough swarm can be as visible as its creators want. Light can be directed towards the planet, which is probably the most effective way to announce its presence, and a large enough and dense enough swarm will block out stars in a particular region of the sky.
There's a tradeoff to be made between swarm density and keeping the engineering difficulties of keeping the planet illuminated and a fancy shape visible, so let me suggest something rather different.
The oft-mentioned Nicoll-Dyson Laser is generally brought up as a means to blast people at stupendous distances, but it could also be used to illuminate a planet. Basically you fit an optical phased array laser to the non-collecting side of each swarm element, that lets you emit beams of light of varying powers and directions (and depending on how your array works and your tech level) different frequencies, too.
This would let you have a sun of almost arbitrary shape and colour, because what the planet sees isn't a star at all but in fact a stellar-scale lightshow.
Just the shape of a an animal? Pah, think bigger! Imagine the sun appearing as an actual animated face! Think of the fun you could have.
Any by way of a bonus you can smite your enemies even if they're a million lightyears away. What's not to like?
